Abstract

We develop thermodynamic models for discrete-time
large-scale dynamical systems. Specifically, using compartmental
dynamical system theory, we develop energy flow models possessing
energy conservation, energy equipartition, temperature
equipartition, and entropy nonconservation principles for
discrete-time, large-scale dynamical systems. Furthermore, we
introduce a new and dual notion to entropy; namely,
ectropy, as a measure of the tendency of a dynamical
system to do useful work and grow more organized, and show that
conservation of energy in an isolated thermodynamic system
necessarily leads to nonconservation of ectropy and entropy. In
addition, using the system ectropy as a Lyapunov function
candidate, we show that our discrete-time, large-scale
thermodynamic energy flow model has convergent trajectories to
Lyapunov stable equilibria determined by the system initial
subsystem energies.